Tuesday, March 18, 2014

BICEP2 might have detected gravitational waves

BICEP2 team has announced a detection of gravitational waves via the effects of gravitational waves on the spectrum on polarization of cosmic microwave background (CMB). What happens that gravitational waves (or possibly some other mechanism) transforms so called E modes which correspond the curl free part of polarization field expressible as gradient to B modes responsible for the divergenceless part of polarization field expressible as curl of vector field.

Interaction of photons with gravitons would induce this polarization changing transformation: this is discussed in earlier post by Lubos. The signal is unexpectedly strong constraints on possible models, in particular to the inflationary models which are currently in fashion. There is excellent popular summary of the physics behing scalar, vector, and tensor perturbations of CMB here. The map produced by BICEP describes the vorticity of the polarization field at the sky and one can clearly see it.

There has been a lot of pre-hype about the finding as proof for inflation, which it is not. Even Scientific American falls in the sin of inflationary hyping which is a pity. Inflationary theory is only the dominating theory which might be able to explain the finding.

In the following the findings are discussed in the framework of TGD based cosmology in which the flatness of 3-space is interpreted in terms of quantum criticality rather than inflation. The key role is played by gradually thickening cosmic strings carrying magnetic monopole flux, dark energy as magnetic energy and dark matter as large heff phases at cosmic strings. Very thin cosmic strings dominate the cosmology before the emergence of space-time as we know it and quantum criticality is associated with the phase transition between these two phases. Later cosmic strings serve as seeds of various cosmological structures by decaying partially to ordinary matter somewhat like inflaton fields in inflationary cosmology. Cosmic strings also explain the presence of magnetic fields in cosmos difficult to understand in standard approch. The crucial point is that - in contrast to ordinary magnetic fields - monopole fluxes do not require for their creation any currents coherent in long scales.

Liam McAllister's summary about the findings of BICEP2 team

Liam McAllister from Cornell University has written an excellent posting about the discovery and its implications in Lubos's blog. McAllister discusses the finding from several points of view. Can one trust that the finding is real? How should one interpret the result? What are its implications? A brief summary is in order before going to details.

  1. Consideration is restricted to inflationary scenarios but it is made clear that they are not the only option. It is emphasized that a huge amount of inflationary parameter space is excluded by the unexpectedly high strength of the effect. Also the general problems of inflationary models are made explicit - a great favor for those who are not inflationary enthusiasts and might have something else in mind.

  2. Also other than gravitonic mechanisms transforming E modes to B modes can be imagined. For instance, the signal might not be primordial but caused by polarized foreground sources: BICEP claims that these contributions have been eliminated.

  3. The most important conclusion is of course that a direct detection of gravitational waves - maybe even quantal ones - has been achieved. Earlier gravitational radiation has been detected only a slowing down of rotation rate of pulsars (Hulse-Taylor binary pulsar).

Comparison of inflationary models and TGD

Further conclusions depend on the cosmological model adopted and McAllister considers the situation in the framework of inflationary models and lists the basic aspects of inflationary model.

  1. The Universe on large scales should be approximately homogenous, isotropic and flat.

  2. The primordial scalar density perturbations should be correlated on super-horizon scales and be approximately Gaussian, adiabatic, and approximately scale-invariant.
In TGD framework inflationary cosmology is replaced with a cosmology fixed almost uniquely by the criticality of the mass density when combined with imbeddability to N4× CP2 as Lorentz invariant 4- surface. The only free parameter is the finite durationkenotau of the critical period. This kind of critical - it seems even quantum critical - periods are predicted to appear in various scales so that Russian doll cosmology is strongly suggested as in case of inflationary models. Scalar fields (inflaton fields) are replaced with cosmic strings, which evolve by thickening their M4 projections from string world sheets to 4-D ones. Magnetic energy replaces dark energy and has interpretation as counterpart for the energy of inflation field. Dark matter at magnetic flux tubes corresponds to large hbar phases (see this , this , and this ).
  1. In TGD framework the long range correlations would be due to quantum criticality rather than extremely rapid expansion during inflationary period. The Universe in large scales should be also now homogenous, isotropic, and flat.

  2. The primordial density perturbations reflect the presence of cosmic strings (see this) before the phase transition period. These cosmic strings have 2-D M4 projection, which is minimal surface, so that these object behave for all practical purposes like strings, and CP2 projection is e 2-D holomorphic surface in CP2. During primordial period cosmic strings dominate and the mass density behaves like 1/a2, where a is proper time coordinate of the light-cone. The mass per comoving volume goes to zero at the moment of big bang so that initial singularity is smoothed out and big bang transforms to "a silent whisper amplified to big bang". For radiation dominated cosmology mass density would behave as 1/a4 giving rise to infinite energy per comoving volume at the moment of Big Bang.

  3. Cosmic strings gradually thicken their M4 projections and the huge primordial magnetic fields carrying quantized monopole flux weaken. These fields differ crucially from the ordinary magnetic fields in that no current is needed to create them - this is due the fact that CP2 Kähler form defines a self-dual magnetic monopole (instanton). Amazingly, even the magnetic fields penetrating to super-conductors could be this kind and perhaps even those associated with ferromagnets.

    This can explain why primordial and recent Universe is full of magnetic fields in length scales, where they should not exist since the currents creating them cannot exist in long scales. The thickening of the remnants of cosmic strings would give rise to birth of galaxies organised like pearls in necklace along big cosmic strings: galaxies are indeed known to be organized into long string like structures and density perturbations would correspond to these strings.

    No vacuum expectations of Higgs like scalar fields are needed. Even in elementary particle physics Higgs expectation is replaced with string tension assignable to string like structures accompanying elementary particles.

    Cosmic strings would carry dark energy as magnetic energy and dark matter as phases with large values of Planck constant coming as integer multiple of ordinary Planck constant. Ordinary matter would be formed when cosmic strings and dark matter "burn" to ordinary matter: this would be the TGD counterpart for the decay of inflaton field to ordinary matter.

  4. Cosmic strings would define the density perturbations having correlations on super-horizon scales. In the first approximation they are certainly Gaussian. Whether they are adiabatic (no exchange of heat with environment) is an interesting question: if they correspond to large values of Planck constant, this is certainly what one expects. The perturbations would be approximately scale invariant: p-adic length scale hypothesis would formulate this quantitatively by replacing continuum of scales with a hierarchy of discrete p-adic length scales coming as powers of square root of 2 (half octaves).

  5. One can of course ask about spectrum of Planck constant coming as integer multiples of ordinary Planck constant: could it realize the presence of large number of length scales characterizing criticality? Could the spectrum of length scales implied by spectrum of Planck constants be the TGD counterpart for the inflationary expansion? Does the average value of Compton length or flux tube length proportional to heff=nh increase with exponential rate during quantum criticality as larger and larger Planck constants emerge?
It seems that at this qualitative level TGD survives basic tests at qualitative level but without assuming inflation fields and exponentially fast expansion since quantum criticality predicting flat 3-space (dimensional parameters such as curvature of 3-space vanish). Cosmic strings would represent the long range fluctuations. A further bonus is that cosmic strings explain dark energy and dark matter, and also the presence of long range magnetic fields in cosmos.

Fluctuations of gravitational field

McAllister gives a nice overall summary about the physics involved if given by inflationary models.

  1. It is not yet fully clear whether the fluctuations of gravitational field are quantum mechanical or classical. In TGD framework quantum classical correspondence suggests that quantal and classical identifications might be equivalent.

  2. Just as the quantum fluctuations of inflaton field would give rise to the density fluctuations visible as temperature anisotropies and large scale structures, the quantum fluctuations of gravitational field would give rise to the observed B modes in inflationary scenario. The correlation functions of gravitons in the background metric would tell everything. The problem is that we do not yet have quantum theory of gravitation allowing to really calculate everything except in QFT approximation.

  3. In TGD framework the fluctuations should physically correspond to cosmic strings and the question is whether gravitons can be identified as massless modes for the cosmic strings so that string like objects would give all. In fact, elementary particles are in TGD framework identified as string like objects! Ironically, TGD as generalization of string model realizes stringy dream in all scales and even for ordinary elementary particles!
Since gravitons couple to energy the formula for the energy density at which inflationary period begins should determine the spectrum of gravitational waves. Inflationary models predict this energy scale as the fourth root of the energy density in the beginning of inflation: the formula is given by in the article of McAllister. This formula contains single dimensionless parameter called r, and BICEP measurements give a rather large value r=.2 for it.

The natural expectation is that any theory explaining the findings in terms of gravitons produces similar prediction but with the energy density of scalar field replaced with something else. In TGD the energy density assignable to cosmic strings so that the square root of the energy density of cosmic string multiplied by some numerical factor should be the relevant parameter now.

Inflation should begin at GUT mass scale

The first implication of the findings is that if inflation explains the findings, it should have begun in GUT scale 1016 GeV, which is very high. The findings cut off a gigantic portion of the parameter space of inflationary models and leaves only inflation potentials that are approximately translationally invariant.

In TGD framework one expects that the energy scale corresponds to that in which quantum critical period begins after string dominated primordial period. This scale should be given by CP2 mass scale apart from some numerical factor. CP2 mass corresponds to m(CP2)=hbar/R(CP2), where R(CP2) is CP2 radius. p-Adic mass calculations predict the value of electron mass and assign to electron the largest Mersenne prime M127 having the property that the p-adic length scales kenosqrtpR(CP2) is not completely super-astronomical. This fixes R(CP2) and m(CP2). The outcome is m(CP2)∼ 4× 1015 GeV.

A numerical constant can be present in the estimate for the energy scale at which quantum critical period begins. In particular, the factor 1/αK1/4 should be present since Kähler action is proportional to 1/αK, which by simple argument is in excellent approximation equal to the inverse of the fine structure constant equal to 137. This would rise the estimate for the energy scale to about 1016 GeV if the same formula for it is used also in TGD (which might of course be wrong!). With a considerable dose of optimism one could say that TGD allows to understand why the measured value of r is what it is.

Difficulties of the inflationary approach

What is nice that McAllister discusses also so the difficulties of inflationary approach.

  1. So called Lyth bound gives lower bound for the distance that inflaton's vacuum expectation must move in field space in order to generate detectably large primordial waves: that is the duration of the inflationary expansion. The lower bound is given by Planck mass MP: Δ Φ >MP.

  2. There is however a problem. This distance should be not larger than the cutoff scale Λ of the quantum field theory. But if standard wisdom is taken granted, Λ should be smaller than Planck mass MP giving Δ Φ<MP!

  3. One can certainly invent all kinds of tricky mechanisms to circumvent the problem: the proposal considered by McAllister is that the couplings of Φ are suppressed to heavy degrees of freedom so that the UV theory respects the approximate shift symmetry Φ→ Φ+Δ Φ. This is true for massless scalar field but this field does not develop vacuum expectation value. McAllister mentions that for V=m2Φ2/2 the approximate shift symmetry is true. Maybe it is for small enough values of m: exact symmetry would require m=0 .

  4. The physical interpretation of masslessness implied by strict shift invariance would be in terms of conformal invariance. In TGD framework quantum criticality implies conformal invariance also in 2-D sense and quantum criticality corresponds to the absence of dimensional parameters from Higgs potential making Higgs mechanism impossible.
To my humble opinion, this difficulty means a strong blow against the idea about Higgs mechanism as source of vacuum energy density in cosmology. As already mentioned, the decay of the dark energy identifiable as magnetic energy and large heff dark matter associated with the evolving primordial cosmic strings would produce ordinary matter in TGD Universe.

Also the ordinary Higgs mechanism is plagued by the loss of naturalness and predictivity by the fact that the Higgs particle has too low mass and SUSY has not been found in low enough mass scales to stabilize Higgs mass. In TGD framework the string tension of string like objects assignable to elementary particles would give the dominating contribution to gauge boson masses and p-adic thermodynamics in its original form the dominating contribution to fermion masses (see this and this). The couplings of fermions to Higgs are gradient couplings and the coupling is same for all fermions in accordance with naturality and universality.

The overall conclusion is that TGD survives the new findings at qualitative and even partially quantitative level.

For details see the chapter TGD and Cosmology of "Physics in Many-sheeted Space-time" , or the article BICEP2 might have detected gravitational waves.

34 Comments:

At 2:53 AM, Blogger Leo Vuyk said...

Hi Matti,

Congratulations with your alternative approach giving dark matter and dark energy a central role:
quote:
"Magnetic energy replaces dark energy and has interpretation as counterpart for the energy of inflation field. Dark matter at magnetic flux tubes corresponds to large hbar phases."

 
At 5:30 AM, Anonymous Matti Pitkanen said...


Thanks. This approach solves a whole bundle of problems usually thought to be unrelated providing also a model for the formation of galaxies and generation of galactic magnetic fields.

 
At 6:55 AM, Blogger Leo Vuyk said...

I am also convinced, however How you could make it more approachable."
I made a suggestion earlier called:

The Splitting Dark Matter- Black Hole- Big Bang and the Cyclic Multiverse
http://vixra.org/pdf/1306.0065v2.pdf

 
At 1:41 AM, Anonymous Matti Pitkanen said...

Concerning your approachability question there is
no answer. One must just wait that the time becomes ripe. The existing paradigms have reached dead end and this eventually motivates people to look for alternatives.

You talk about lattices: this notion is very interesting as lattice associated with hyperbolic space (cosmological time =light-cone proper time =constant section of M^4 in TGD). The lattices correspond to subgroup of SL(2,C) and are extremely interesting mathematically.

Quantization of redshifts and directions of cosmic recession velocity for astrophysical objects is the physical counterpart for the lattice and there is some evidence for quantisation of redshfts - so called God's fingers.

 
At 7:29 AM, Blogger Leo Vuyk said...



Together with the axis of evil related to the cold spot, the dipole modualtion ( DM or Hemispherical PA Power asymmetry or dipole variations of the Wmap are reason to designe an other Bang. called:
The Splitting Dark Matter- Black Hole- Big Bang and the Cyclic Multiverse
http://vixra.org/pdf/1306.0065v2.pdf

 
At 7:50 AM, Blogger Leo Vuyk said...

So we seem to live inside a pear shaped egg with a cold spot at the start and we look at the WMAP as the result of the last splitting and evaporating black hole splinters of the BIg Bang black hole. These splinters larger at the start around the cold spot and smalerl at the opposite side of the pear.see: http://arxiv.org/pdf/1402.0870v2.pdf

 
At 10:36 PM, Anonymous Matti Pitkanen said...


These anomalies in long scales could be seen as signatures for the existence of large scale structures much large than horizon. If I understand correctly, you assign them to those multi-blackhole structures.

In TGD picture they would be very long cosmic strings - or more precisely- they remnants responsible for very long range magnetic fields. This in principle is a test for their identity.


Distributions of dark matter and dark energy ( magnetic energy) should reflect the distribution of gradually thickening cosmic strings. FEssentially free motion of matter along along string like objects is another prediction: this kind of motions have been detected.

Fractality means that strings would make themselves visible at the dynamics of galaxy: some evidence that our galaxy corresponds to a node of two intersecting cosmic strings, exist. Even solar systems might involve cosmic string along which dark matter travels to/from some other star: some evidence exists also for this.

There is evidence for similar fractal nets of magnetic flux tubes in living matter: they would be crucial for the morphogenesis and morphostasis. For example, replication of DNA, cell, even simple organism like planaria when its is split into two pieces and pieces develop a new head/tail could be basically due to the replication of the grid like magnetic body coding for both structure and function - the latter meaning that also the learned behaviors are inherited and possessed by the planaria, which develops a new head!): there is evidence for this.

This replication vertex for 3-surfaces distinguishes TGD from string models and is analog for 3-vertex for Feynman diagrams. It is fascinating that it would be crucial for understanding the fundamental signature of living matter. I have talked about this in earlier posting.

 
At 1:27 AM, Blogger Leo Vuyk said...

So the peucliar differences in magnetic structures are in line with TGD., but are the other structures also?
As there are :
axis of evil related to the cold spot, the dipole modualtion ( DM or Hemispherical PA Power asymmetry or dipole variations of the Wmap ?

 
At 2:21 AM, Anonymous Matti Pitkanen said...


Thank you for asking. I answer very briefly since I heard just some time ago a very sad family news.

To my best knowledge (I am not professional) evolving cosmic strings can explain the known anomalies. One basic prediction is honeycomb structure with cosmic strings at their boundaries along long string like structures. Cold spot would represent almost empty cell of honeycomb with exceptionally large size.

 
At 2:15 AM, Blogger Leo Vuyk said...

I am very sorry for you.

 
At 2:45 PM, Blogger crow said...

Matti, sorry for sadness and its source, etc. :( You mention proper time... and I only came here to link back to http://en.wikipedia.org/wiki/Lorentz_factor and it made me realize I wrote an entry in OEIS.org (online encyclopedia of integer sequences) http://oeis.org/A001790 This sequence gives the numerators of the Maclaurin series of the Lorentz factor (see Wikipedia link) of 1/sqrt(1-b^2)=dt/dtau where b=u/c is the velocity in terms of the speed of light c, u is the velocity as observed in the reference frame where time t is measured and tau is the proper time. - Stephen Crowley, Apr 03 2007

 
At 5:53 AM, Blogger Ulla said...

http://www.pa.ucla.edu/sites/default/files/webform/%20%C2%A0Freese%20inflation%20UCLA.pdf
false and true vacuum, magnetic monopoles...

http://detroit.cbslocal.com/2014/03/20/um-physicist-on-her-big-bang-models-validation-woo-hoo/

http://arxiv.org/abs/hep-th/0504168 linked to supergravity

http://en.wikipedia.org/wiki/QCD_vacuum

 
At 12:17 AM, Anonymous Matti Pitkanen said...


Thank you for empathy. These kind of events really stop.

To crow: The Lorentz factor is indeed quantized if lattice like structures in hyperbolic manifold (mass shell in particle physics) are realised. Fixing subgroup fixes the quantisation rule.

 
At 12:25 AM, Anonymous Matti Pitkanen said...


To Ulla:

There has been a lot of hype around the finding.

The results are seen even as proof of inflation. The guest posting in Lubos's blog told the truth. There is internal contraction plaguing all inflationary models and basically due to the fact that the production of large enough gravitonic background is in conflict with the assumption that quantum field theory works- that is the idealisation as point like particles makes sense.

Also Jester tells the truth

http://resonaances.blogspot.fi/2014/03/curly-impressions.html

and also Matt Strassler:

http://profmattstrassler.com/2014/03/18/if-its-holds-up-what-might-bicep2s-discovery-mean/

To be continued...

 
At 12:27 AM, Anonymous Matti Pitkanen said...


String theory is the next candidate to be hyped after the parameter space for inflationary models has shrinked to zero. The irony is that TGD description reduces essentially to stringy description with quantum criticality added.

For Higgsy massivation the parameter space has already shrinked to to zero but people want to see this as a victory for a brand new world view in which we should accept as a fact that fundamental theories cannot predict anything (multiverse). Physics as science is living hard times now since different camps are desperately fighting for funding instead of trying to find way out of the dead alley.

For standard SUSY the parameter space is also reducing rapidly. Experimentalists are painting poor theoreticians to a corner;-).

Progress cannot be made only before the non-point-likeness of even elementary particles is realized: QFT is simply not enough anymore. In the case if Higgs this means giving up the idea about Higgs vacuum expectation as source of mass.

Ironically, stringy contributions would explain most of gauge boson and Higgs mass and fermion masses would be mostly due to p-adic thermodynamics (which also has real variant but with constraints coming from the condition that it is equivalent with the p-adic variant). This is something very different from string theory but string like objects emerge also now.

Unfortunately, this kind of really big paradigm shifts are very difficult since two many faces would be lost. The funding machinery of Big Science with its enormous inertia. Maybe the situation is totally different after five decades;-)

 
At 4:46 AM, Blogger Leo Vuyk said...

B-Modes and the relation with evaporating big bang black holes:
Max Tegmark:
It turns out that the physical process by which inflation generated these gravitational waves is the same process (discovered by Stephen Hawking) by which black holes evaporate. Whenever there’s an event horizon, quantum fluctuations cause it to emits radiation. For an evaporating hole, you look at its horizon from the outside; in our cosmos, we look at the horizon (basically the region from beyond which light can’t reach us) from the inside. Until today, there was no experimental evidence for Hawking’s prediction – but now there is! :-)

http://www.huffingtonpost.com/max-tegmark/good-morning-inflation-he_b_4976707.html

I like the black hole big bang theory postulated by Neil Turok.
New for me was that he said:
the CMB is in fact the “inside of the expanded evaporating black hole”!! Which also should be cyclic and part of a multiverse.
However Turok should realize that this expanding black hole is perhaps also splitting into smaller black holes accelerated creating the Lyman Alpha tree structure and at the end at extinction moment, these B-Modes and the CMB structure itself even equipped with a starting split like a navel cord, see :
The Navel Cord Multiverse with Raspberry shape.
http://vixra.org/pdf/1312.0143v1.pdf and
The Raspberry Shaped SuperSymmetric Multiverse without a CAT paradox.
http://vixra.org/abs/1308.0083

 
At 4:39 PM, Blogger crow said...

"To crow: The Lorentz factor is indeed quantized if lattice like structures in hyperbolic manifold (mass shell in particle physics) are realised. Fixing subgroup fixes the quantisation rule." Some time ago I titled a section of an unpublished paper "overcoming partially hyperbolic transervality in R^3" does that even make sense or was I out of my mind?"

 
At 5:10 PM, Blogger crow said...

Correction, that should have said "overcoming partially hyperbolic transervality torsion in R^3""

 
At 10:39 PM, Anonymous Matti Pitkanen said...

To crow:

If you mean R^3 in only topological sense but free to have any metric- Euclidian or hyperbolic so that there is no problem. I have used E^3 to denote R^3 endowed with Euclidian metric. H^3 is used when the metric is hyperbolic metric induced from the metric of 4-D Minkowki space to proper time constant hyperboloid of future light-cone.

 
At 2:04 PM, Blogger Ulla said...

Thomas Ryttov and his colleagues at CP ³ - Origins believe that the so-called techni-quarks can be the yet unseen particles, smaller than the Higgs particle. If techni-quarks exist they will form a natural exention of the Standard Model which includes three generations of quarks and leptons. These particles together with the fundamental forces form the basis of the observed matter in the universe.

Read more at: http://phys.org/news/2014-03-particles-smaller-higgs-particle.html

 
At 12:15 AM, Blogger Ulla said...

http://arxiv.org/abs/1403.5166v1

 
At 11:51 AM, Blogger crow said...

Matti, did your email address change? Tried to send you a voice message via email.

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At 2:12 AM, Blogger Leo Vuyk said...

In my view: BICEP-2 -B-Modes are the END of a splitting Fractal Black Hole Big Bang nucleus (singularity) inflation process. So, the Big bang was the splitting and evaporation of the big crunch black hole ( all universal 10^90 particles closely packed inside) into what I call a black hole splitting fractal inflation creating the Lyman Alpha forest structure. What we observe in the B-Modes of the BICEP 2 image should be the END of the Fractal splitting black hole inflation process at the rim of our own Universal bubble as part of the super symmetric raspberry multiverse.
The cyclic universe is a continuous balancing game between dark energy in the vacuum Higgs field and dark matter inside black hole nuclei.
Dark energy is the energetic oscillating Higgs field, dark matter is the particle based (Preon) nuclei of all Black holes, with pair production by fluctuations at the BH horizon.

See: The Navel Cord Multiverse with Raspberry shape.
http://vixra.org/pdf/1312.0143v1.pdf

;

 
At 7:40 AM, Anonymous Matti Pitkanen said...


To Leo Vuyk:

I just wrote a little posting about the inflationary cosmology in TGD framework.

As you know the solution (de Sitter) can be also interpreted as a stationary solution representing the interior of blackhole as volume with constant matter density and finite radius characterising its mass just as in the case of black hole.

It is possible to imbed this as a *completely stationary* vacuum extremal to imbedding space M^4xCP_2 and the imbedding is very natural. This would represent stationary non-expanding cosmology when the radius goes to infinite.

The interpretation as inflationary cosmology results by introducing different coordinates. This interpretation looks in sub-manifold gravity more like a coordinate trick. One just inroduces radial coordinate which is related to the radial Minkowski coordinate by exponentially increasing scaling and gets apparent exponential expansion. In TGD framework inflation does not seem to make much sense: quantum criticality is much more natural interpretation.

The most natural interpretation is as ultra simple model for the interior of stationary astrophysical object. If cosmology is in question it is stationary- a very large space-time sheet carrying constant average mass density. This kind of objects would define a model for space-time sheet containing matter and these space times could form an expanding "gas".

It might be also possible to have the analog of inflation as hbar increasing phase transitions and their reversals but this is a another story. The transitions increasing p-adic prime by powers
of two would replaced e-foldings.

 
At 9:43 PM, Anonymous Matti Pitkanen said...


To crow:

Sorry for not noticing your question. My email address is same as before.

 
At 9:47 PM, Anonymous Matti Pitkanen said...


To Leo Vyuk:

I looked details of critical cosmology and found that also now there is a period of very fast expansion. da/dt goes from very small value to infinity during the Minkowskian period of the induced metric: this period has finite duration.

After that the signature becomes Euclidian and a transition to radiation dominate cosmology is expected to take place as magnetic energy decays to massless particles. Several expanding sheets of radiation dominated cosmology are expected to be generated corresponding to sub-CDs

 
At 5:13 AM, Blogger Leo Vuyk said...

Matti,
you wrote: "now there is a period of very fast expansion."
Is it also possible in TGD that the universe is cyclic? and that the inflation epoch is based on a fractal alike Lyman Alpha forest creating system of something as a splitting black hole?

see :
http://vixra.org/pdf/1103.0002v4.pdf

 
At 3:46 AM, Blogger Sagheer said...

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At 9:27 AM, Blogger Dinesh gir said...

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At 8:10 PM, Blogger daniyal raza said...

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At 8:08 PM, Blogger rashid omer said...

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At 12:03 PM, Blogger Sagheer said...

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At 8:24 PM, Anonymous Matpitka@luukku.com said...

Sorry for this Sagheer/Dines/etc… He causes a lot of trouble. I have hoped that he could find some help to his personal problems. Some kind of father complex probably.

 
At 8:53 AM, Blogger Dinesh gir said...

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